Electrically operated drive systems

ABSTRACT

Electrically operated drive system for driving coaxial shafts comprising two electric motors, two switching circuits for respectively connecting the motors to and disconnecting them from an electrical supply, the switching circuits being each adapted alternately and for variable periods to connect and disconnect the supply to and from the associated motor so that the means power supplied to said associated motor is variable and means for rendering the means power supplied to one of the motors different from that supplied to the other motor.

United States Patent Gurwicz Feb. 29, 1972 [54] ELECTRICALLY OPERATED DRIVE [56] References Cited SYSTEMS UNITED STATES PATENTS [72] 12;: Gateshead Dumam' 3,199,008 8/1965 Stone ..31a/so 8 3,447,050 5/1969 Geis ...3l8l67 [731 Assignees: Sevcon Engineering Limited; Ransomes 3,534,239 10/1970 Risberg ..3l8l52 Sims & Jeiieries Limited Primary Exantiner-Bemard A. Gilheany [22] 1970 Assistant ExaminerW. E. Duncanson, Jr. [2]] Appl, NO 32,689 Attorney-Ira Milton Jones Related Us. Application om 57] ABSTRACT [63] Continuation-impart of Ser. No. 682,468, Nov. 13, Electrically operated drive system for driving coaxial shafts 1967, abandoned. comprising two electric motors, two switching circuits for v respectively connecting the motors to and disconnecting them [30] Foreign Application Priority Data from an electrical supply, the switching circuits being each adapted alternately and for variable periods to connect and Nov. 14, 1966 Great Britain ..51,010/66 disconnect the supply to and from the associated motor so the means power supplied to said associated motor is variable [52] US. Cl "318/67 and means for rendering the means power supplied to one of [5 l Int. Cl. ..H02p 7/ 68 the motors different from that Supplied to the other match [58] Field oiSearch ..3l8/52,67, 68,80

11 Claims, 5 Drawing Figs.

PULSE GENERATOR l 1 A MOTOR I 1 ACCELERATOR D m L SA UN |T UN IT l 6 moron SB 5 l l PULSE GENERATOR l w e 1 l SUPPLY ACCELERATOR DIFFERENTIAL PATENTEUFEBZQIHYZ Y 3,646,414

. SHEET 1 OF 3 PULSE GENERATOR MOTOR UNIT UNIT

MOTOR PULSE swam-r023 I 0 c I SUPPLY P,

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R! AF OB TO PULSE To PULSE GENERATOR A GENERATOR B 175F10 Fvrmaz igimi PATENTEIJFEB29 1972 I 3, 45,414

SHEET 2 BF 3 T0 TRANSISTOR T121 TO TRANSISTOR T122 v A vvv 5 T0 PULSE H TO PULSE GENERATOR A GENERATOR 5 TIZI TR2 vRl W o a A TO PULSE TO PULSE GENERATOR 5 GENERATOR A 17.012201 Fur z 2% 1 ELECTRICALLY'OPERATEDDRIVE'SYSTEMS This application is a continuation-in-part of my copending application'Ser. No. 682,468,"filed Nov. 13, 1967 now abandOl'l'Cd;

This invention relates to electrically operated drive systems. More particularly, theinventionis concerned with electrically operated'drive systems of thekind in which coaxial shafts are capableof being'supplied with different driving power to enable'a r'nember driven by the'drive system to move along a curved-path.

It is well known that the differential action required when the two driven wheels on a vehicle have to negotiate a curve or comer, can be provided by the use of two DC series wound electric drive motors driving each of the wheels in question. These motors are connected in sucha manner that the current flowing in each of the motor armatures is the same at all times. The preferred method of obtaining this result is to connect the two armatures in question in series across the supply. in this case the retardation of the inside motor does not result in excess current flow through it, since the current is limited by the corresponding increase in speed of the outside motor. The above system, however, suffers the defect of all such differential systems inithatif one of the driven wheels loses its adhesionto the surface on which it drives, the complementary motor is unable to product any driving torque;

One object of this invention is to provide an electrically operated drive system of the kind set forth in which the abovementioned disadvantage is overcome.

The present invention consists in an electrically operated drive-systemof the kind in which coaxial shafts are capable of being supplied with different driving power to enable a memberdriven by "the drive system to move along a curved path, comprising two electric motors, two switching circuits for-respectively connecting the motors to and disconnecting themotors fromelectrical supply means, saidswitching circuits being each adapted alternately to connect the supply means to and disconnect the supply means from the associated motor and being further adapted to vary the ratioof the time of connection to and disconnection from the associated motor thereby to vary the mean power supplied to said associated motor, and means for so varying said ratio for at least one of the motors as to render different the power supplied to each motor.

In one form of the invention the means for so varying the ratio of the time of connection to and disconnection from the supply means of at least one of the motors are adapted to maintain substantially constant the power supply to one of the motors while varying'the power supply to the other motor below the value of the supply to said one motor.

In another form of the invention the means for so varying An arrangement as justset forth affords all the advantages of an electrical differential arrangement and at the same time avoids the disadvantage previously described. Furthermore, by a suitable arrangement, the pulse generators can be utilized for stepless, loss free speed control of the vehicle.

The invention will now be described by way of example with reference to the accompanying drawings, which relate to electrical drive systems which are suitable for the control of the mean power, derived from the DC power source P, by motor.

A. Similarly pulse generator B controls motor B. Motors A and B drive respective coaxial shafts SA and SB carrying, e.g., the driving wheels of a vehicle. Both these pulse generators 7 respond to a voltage input signal of zero to V volts, for example. With a zero voltage input signal to either pulse generator, that pulse generator is quiescent and zero poweris supplied to the load, i.e., the associated motor and with an input signal of V volts to either pulse generator, that pulse generator causes the supply of maximum power to the associated motor. An intermediate voltage signal to either pulse generator will result in a correspondingly, reduced power supply to the associated'motor. A differential unit Dis so arranged as to accept an input signal of between zero and V" volts from an accelerator unit E and to supplypulse generator 1 units A and B with an input signal which is a function of both the ratio of the time of connection to and disconnection from the supply means of at least one of the motors are adapted to maintain substantially constant the power supply to one of the motors'while varying the power supply to the other motor above the value of the supply to said one motor.

in a'furth'er form 'of the invention the means for so varying the ratio of thetime of connection to and disconnection from the supplymeans of at least meet the motors are adapted simultaneously'to reduce the power supply to one motor while increasing the supply to'the other motor.

Suitably, control means are afforded for simultaneously varying in like manner the ratio of the time-of connection to disconnection from the supply means, of each of the motors therebysimultaneously'to increase or decrease the mean current througheach motor.

Preferably the switching circuits include semiconductor staticswitching devices to effect connection to and disconnection from the electrical supply means of each motor.

In the'caseof an electrically operated vehicle drive system, the motorsare'usuallyDC series wound motors but could be shunt or compound wound motors and the means for varying the'output signal from each pulsegenerator circuit are actu-- ated upon movement in oneor the opposite sense from a central position of the vehicle steering member.

the accelerator unit output voltage and the position of the vehicles steering mechanism. With the steering mechanism set to a central position, for example, and an accelerator unit input signal of v volts say, where v is less than V the differential unit will supply an input signal of v" volts to each of the pulse generators A and B. If, however, the steering mechanism is adjusted'to provide an amount of turn,-then with an accelerator unit signal of v volts, the differentialunit will supply pulse generator unit A with \rhSv" volts and v-Sv" volts to pulse generator B. It will be understood that in these circumstances motor B drives the radially inner wheel of the arc of turn of the vehicle. The value of 8v is proportional to the amount of turn demanded by the steering mechanism.

Referring now to FIG. 2, the differential unit is supplied from a voltage source of magnitude in excess of 2V volts. VRl

is the accelerator unit E. R1 is provided to limit the maximum excursion of the voltage at the wiper arm of VRl to V" volts below'the positive supply potential. The transistors TR! and TR2 are as shown of the PNP kind and are supplied with a common base-potential from the wiper arm of VR'l. Resistors R2and R3 are equal and are half the value of VRZ which is a potentiometer having a wiper arm mechanically coupled to the steering mechanism of the vehicle. For an accelerator unit output signal of v" volts wherev V, the bases'of TRl and TRZ will be held at this voltage below the positive supply potential. The collector current flowing in each transistor will be approximately given by v/R2 amps. With the wiper arm of VR2 in the mid position the potential appearing at the collectors of TR'l'AND TRZ will be given by the collector current in each case multiplied by half the resistance of VRZ, i.e., v" volts. This signal will be fed to both pulse generators A and B. Any deviation of the wiper from the midposition of VR-2 will result in the reduction in input signal to one side and increase of signal to the other. At the limit the input signal to one pulse generator will be zero and to the other 2 v volts. It will,

therefore, be appreciatedthat differential action can be obtained in conjunction with normal variable speed control from the accelerator unit.

In the circuit arrangement shown in FIG. 3 the wiper armof that as the wiper arm is moved by adjustment of the vehicle steering mechanism from its midposition, the input voltage to one of the pulse generators, depending on which side of the midposition the wiper arm is moved, is reduced while the input voltage to the other pulse generator remains constant. In this arrangement, therefore, adjustment of the steering mechanism effects reduction of the power supplied to the motor driving the wheel which is radially inwardly disposed with respect to the center of curvature of the vehicle path while the power supply to the other motor remains constant.

In the circuit arrangement of FIG. 4, the potentiometer VR2 is inserted in the emitter system of the transistors TR! and TR2 and the wiper arm of the potentiometer VR2 is connected to a center tap of the resistor of the potentiometer. It will be seen that at any given value of input voltage applied to the connected bases of the transistors, movement of the wiper arm of potentiometer VR2 from the central position thereof has the effect of increasing the emitter current of one of the transistors while that of the other transistor remains constant. The input voltage to the pulse generator connected to the transistor whose emitter current has increased is therefore also increased while the input voltage to the other pulse generator remains the same. The power supplied to one of the motors is thus increased while that supplied to the other motor remains constant.

In the embodiments of the invention described above, the accelerator unit, the pulse generator of each motor and its associated static switching devices for effecting connection to and disconnection from the supply of the motors is fully described, for example, in US. Pat. No. 3,222,582, which shows a DC motor fed from a battery through a silicon controlled rectifier, there being provided a transistor oscillator to supply triggering pulses to the gate electrode of the silicon controlled rectifier and communicating means for turning off the silicon controlled rectifier at a predetermined time after it has been switched on by a triggering pulse. The frequency of pulses supplied by the oscillator, and hence the ratio of time of connection to and disconnection from the battery of the motor, is controlled by a variable resistor in the oscillator circuit, but obviously in the present case the frequency of operation of each pulse generator would be controlled by the input voltage to the pulse generator. An example of an accelerator unit in which this is done is described more particularly in US. Pat. No. 3,337,786. Examples of static switching circuits including pulse generators such as A and B are also described in detail in US. Pat. Nos. 3,297,931 and 3,365,640.

It will be appreciated by those skilled in the art that alternative methods to those described above exist for effecting the requisite control of the motor 1 of the drive system to enable curves to be negotiated.

An example of a suitable circuit for pulse generator A is shown in H0. 5. In this circuit, motor A is connected to the DC supply through diode RDl and main thyristor SCRl, the gate electrode of which is fed with firing pulses from an oscillator comprising capacitor C3, transistor TR3 and transistors TRl and TR2. The base of the transistor TRS receives the input voltage v from point A of the differential unit D. As- I sociated with the main thyristor SCR! is a commutating circuit comprising capacitor CE, inductor Ll, diode D3 and thyristor SCR3, the gate electrode of which receives firing pulse from an oscillator comprising transistor Q3 and Q4, capacitor C2 and resistor R11. The operation of the circuit is as follows. When main thyristor SCRl is rendered nonconducting by the commutating circuit, a voltage approximately equal to that of the supply is applied cross capacitor C3 and transistor TR3, and the capacitor begins to charge at a rate determined by the degree of conductance of transistor TR3. The potential of the plate capacitor C3 connected to the collector of transistor TR3 thus falls, and when this potential falls I below the fixed potential at the junction of resistors R7 and R8, transistor TR2 begins to conduct. The potential at the base of transistor TR] thus falls and this transistor also is switched into conduction. Capacitor C3 then discharges rapidly through transistor TR! and TR2 and the primary winding T1 of a transformer, from the secondary winding T2 of which a pulse of current is fed to the gate electrode of thyristor SCRl, thus rendering this thyristor conducting and connecting motor A to the DC supply. It will be apparent that the time which elapses between thyristor SCRI becoming nonconducting and its being switched into conduction again is dependent on the rate of charging of capacitor C3 and therefore on the voltage applied to the base of the transistor TR3, i.e., the input voltage signal V from the differential unit D.

During the period in which thyristor SCR] is nonconducting, commutating capacitor CE is charged through thyristor SCR3, which becomes noneondueting when CE is fully charged and the charging current through thyristor SCR3 falls to zero. At the same time capacitor C2 becomes fully charged through diode-D1. When thyristor SC! is rendered conducting, capacitor CE discharges through the oscillatory path ineluding thyristor SCRl, inductor L] and diode D3, and recharges with reversed polarity, the reverse charge being retained by diode D3. At the same time, capacitor C2 begins to discharge through resistor R11 and thyristor SCR]. When the potential of the junction of capacitor C2 and resistor R11 falls below that of the emitter of transistor Q3, this transistor is switched into conduction, and transistor O4, is therefore rendered conducting. Current from line P, which is held at a positive potential V1, therefore flows through transistor 04 to the gate electrode of thyristor SCR3 which is rendered conducting. The reverse voltage across capacitor CE is thus applied to thyristor SCRl which is thereby rendered nonconducting. The sequence of events is then repeated. Thus motor A is alternately connected to and disconnected from the DC supply, the periods of conduction to the supply being of constant length and the periods of disconnection from the motor being variable in dependence on the input voltage supplied to the circuit by the differential unit D.

The circuit of pulse generator B is identical with that of pulse generator A, and is therefore not shown in the drawings.

For example, electrical signals could be derived from the voltages appearing across the motor armatures, these voltages varying in accordance with the load on each motor. The signals so derived would then be employed to control the pulse generators A and B and hence the power supplied to their associated motors.

Another method of control is to replace the DC supply in FlGS. 2 to 4 with high frequency alternating current supply derived for example from an inverter. The potentiometer is replaced with two ganged variable capacitors the shaft con-' necting which is mechanically linked with the steering mechanism. The capacitors are so arranged that rotation of their connecting shaft in either sense effects increase in the capacitance of one and corresponding decrease in the capacitance of the other capacitor. The capacitors could also be arranged so that the shaft rotation in either sense effected change in the capacitance of one capacitor while leaving the capacitance of the other capacitor unchanged. In operation of this alternative the collector current of each of transistor TRl and TR2 is an alternating current of frequency the same as that of the supply and of amplitude which depends upon the arrangement of the ganged capacitors and the position of their common connecting shaft.

As an alternative tousing capacitors there can be used two inductor coils through which extends a movable ferrite rod the position of which is controlled by the vehicle steering mechanism. When the vehicle is travelling rectilinearly the ferrite rod is symmetrically disposed with respect to the coils so that the inductanees of the coils and therefore their impedances are equal and equal voltages are therefore derived to supply the pulse generators A and B. However, on attempting a curve the ferrite rod is moved by the steering mechanism to give a greater penetration thereof into one coil than the other. The inductance of one coil therefore increases and that of the other coil decreases with the result that differential voltages are supplied to the pulse generators A and B to control appropriately the power supplied to each of the motors. The ferrite rod can be arranged with ferrite extensions which in the symmetrical position of the rod project respectively beyond the ends of the coils remote from the common connected ends thereof. In this arrangement the movement of the ferrite rod from the symmetrical or means position has the effect that the inductance in one coil is reduced while that of the other coil remains constant. The effect of moving the ferrite rod where the coils are in the collector system of the transistors is therefore to reduce the voltage amplitude supplied to one pulse generator leaving that supplied to the other pulse generator constant. With the coils in'the emitter system of the transistors the effect is to increase the voltage amplitude supplied to one pulse generator leaving that supplied to the other pulse generator constant. I

Another method of obtaining the requisite control effect on the motors is mechanically to couple optical wedges to the steering mechanism, the wedges moving on adjustment of the steering mechanism relatively to photosensitive cells or other devices with the result that current flow through the cells on other devices is varied in desired manner to give any one of the types of control described in relation to FIGS. 2 to 4.

. Yet another method of achieving the requisite form of control is to employ two l-lalleffect semiconductor devices so that on movement from a mean position relative to the devices of a magnet mechanically coupled to the steering mechanism the Hall effect voltages generated in the devices are differentially effected. By appropriate use of the Hall effect devices the different forms of motor control described in relation to FIGS. 2 to 4 are achieved.

Those skilled in the art will appreciate that though the pulse generators are, as described in the patents referred to, of the kind which generate a train of square pulses, they could equally well be of the kind which generate an alternating, for example sinusoidal or saw tooth, voltage which is superimposed on a DC voltage level. The thyristor switches which connect the supply to and disconnect the supply from the motors would be rendered conducting each time the generator voltage increased above the DC voltage level. By varying the DC voltage level the ratio of the time of connection to and disconnection from the supply of the associated motor is varied.

Those skilled in the art will appreciate that the invention can be embodied in forms other than as herein disclosed for purposes of illustration.

The invention is defined by the following claims:

1. An electrically operated differential drive system for enabling a member driven by the drive system to move along a curved path, comprising guiding means for effecting movement of said member along a curved path, two DC electric motors each drivingly connected to said member so that the two motors operate at different relative speeds when the member moves along a curved path in response to the guiding means, electrical supply means, a switching circuit connected between each motor and the supply means for alternately connecting the supply means to and disconnecting the supply means from the associated motor, each switching circuit including ratio varying means responsive to an input signal for varying the ratio of times of connection to and disconnection from the motor thereby to vary the mean power supplied to the motor, and differential means controlled by said guiding means and operatively connected to the ratio varying means of said switching circuits to supply a variable input signal to at least one of said circuit for varying the said ratio for the circuit, thereby rendering different the mean power supplied to each motor.

2. A drive system as claimed in clam 1, wherein the differential means simultaneously supplies an input signal to the ratio varying means of one of said switching circuits to increase the mean power supplied to the associated motor and an input signal to the ratio varying means of the other of said switching circuits to reduce the mean power supplied to the associatedmotor.

3. A drive system as claimed in claim 1, wherein the differential means supplies a constant input signal to the ratio varying means of one of said switching circuits to supply constant power to the associated motor and an input signal to the ratio varying means of the other of said switching circuits to vary the mean power supplied to the associated motor below the value of said constant power.

4. A drive system as claimed in claim 1, wherein the differential means supplies a constant input signal to the ratio varying means of one of said switching circuits to supply constant power to the associated motor and an input signal to the ratio varying means of the other of said switching circuits to vary the mean power supplied to the associated motor above the value of said constant power. 1

5. A drive system as claimed in claim I, wherein there is provided accelerator means operatively connected to the ratio varying means of both said switching circuits'for simultaneously increasing or decreasing the power supplied to each of said motors.

6. A drive system as claimed in claim 1, wherein the differential means includes two transistors the output currents of which provide the said input signals to the ratio varying means of said switching circuits.

7. A drive system as claimed in claim 1', wherein the switching circuits each include semiconductor static switching means to effect connection to and disconnection from the electrical supply means of each motor.

8. An electrically driven vehicle supported on steerable ground-engaging means and having a pair of ground-engaging traction members driven by coaxial shafts, and a differential drive system as claimed in claim 1, said coaxial shafts being drivingly coupled to said DC electric motors of the drive system, and said guiding means constituting the steering mechanism of the vehicle operatively connected to said steerable ground-engaging means.

9. A drive system as claimed in claim 8, wherein the electrical supply means of the vehicle comprises a battery which by way of the switching circuits energizes respective DC, preferably series, motors.

10. An electrically operated drive system for supplying differential driving power to two coaxial shafts to enable a member driven by the drive system to move along a curved path, comprising two electric motors each drivingly connected to one of said shafts, electrical supply means, a switching circuit connected between the supply means and each motor for alternately connecting it to and disconnecting it from the supply means, each switching circuit comprising a main thyristor in series with the associated motor and the supply means and first switching means for rendering the thyristor conducting to connect said motor to the supply means, commutating means connected to the thyristor and second switching means for causing the commutating means to commutate the thyristor to disconnect said motor from the supply means, said switching circuits including ratio varying means responsive to an input signal for controlling said switching means to vary the ratio of the time the motor is connected to and disconnected from the supply means thereby to vary the mean power supplied to the motor, and differential means operatively connected to said ratio varying means to supply a variable input signal to at least one of said switching circuits for varying the said ratio for the circuit, thereby rendering different the mean power supplied to each motor.

11. A drive system as claimed in claim 10, wherein one at least of said switching means comprises a relaxation oscillator including a capacitor and a transistor connected in parallel with the main thyristor, the degree of conduction of the transistor governing the rate of oscillation of the oscillator, said differential means being connected to the transistor to vary the degree of conduction of the transistor in dependence upon the variable input signal supplied by the differential means thereby to vary the rate of oscillation of the oscillator. 

1. An electrically operated differential drive system for enabling a member driven by the drive system to move along a curved path, comprising guiding means for effecting movement of said member along a curved path, two DC electric motors each drivingly connected to said member so that the two motors operate at different relative speeds when the member moves along a curved path in response to the guiding means, electrical supply means, a switching circuit connected between each motor and the supply means for alternately connecting the supply means to and disconnecting the supply means from the associated motor, each switching circuit including ratio varying means responsive to an input signal for varying the ratio of times of connection to and disconnection from the motor thereby to vary the mean power supplied to the motor, and differential means controlled by said guiding means and operatively connected to the ratio varying means of said switching circuits to supply a variable input signal to at least one of said circuit for varying the said ratio for the circuit, thereby rendering different the mean power supplied to each motor.
 2. A drive system as claimed in clam 1, wherein the differential means simultaneously supplies an input signal to the ratio varying means of one of said switching circuits to increase the mean power supplied to the associated motor and an input signal to the ratio varying means of the other of said switching circuits to reduce the mean power supplied to the associated motor.
 3. A drive system as claimed in claim 1, wherein the differential means supplies a constant input signal to the ratio varying means of one of said switching circuits to supply constant power to the associated motor and an input signal to the ratio varying means of the other of said switching circuits to vary the mean power supplied to the associated motor below the value of said constant power.
 4. A drive system as claimed in claim 1, wherein the differential means supplies a constant input signal to the ratio varying means of one of said switching circuits to supply constant power to the associated motor and an input signal to the ratio varying means of the other of said switching circuits to vary the mean power supplied to the associated motor above the value of said constant power.
 5. A drive system as claimed in claim 1, wherein there is provided accelerator means operatively connected to the ratio varying means of both said switching circuits for simultaneously increasing or decreasing the power supplied to each of said motors.
 6. A drive system as claimed in claim 1, wherein the differential means includes two transistors the output currents of which provide the said input signals to the ratio varying means of said switching circuits.
 7. A drive system as claimed in claim 1, wherein the switching circuits each include semiconductor static switching means to effect connection to and disconnection from the electrical supply means of each motor.
 8. An electrically driven vehicle supported on steerable ground-engaging means and having a pair of ground-engaging traction members driven by coaxial shafts, and a differential drive system as claimed in claim 1, said coaxial shafts being drivingly coupled to said DC electric motors of the drive system, and said guiding means constituting the steering mechanism of the vehicle operatively connected to said steerable ground-engaging means.
 9. A drive system as claimed in claim 8, wherein the electrical supply means of the vehicle comprises a battery which by way of the switching circuits energizes respective DC, preferably series, motors.
 10. An electrically operated drive system for supplying differential driving power to two coaxial shafts to enable a member driven by the drive system to move along a curved path, comprising two electric motors each drivingly connected to one of said shafts, electrical supply means, a switching circuit connected between the supply means and each motor for alternately connecting it to and disconnecting it from the supply means, each switching circuit comprising a main thyristor in series with the associated motor and the supply means and first switching means for rendering the thyristor conducting to connect said motor to the supply means, commutating means connected to the thyristor and second switching means for causing the commutating means to commutate the thyristor to disconnect said motor from the supply means, said switching circuits including ratio varying means responsive to an input signal for controlling said switching means to vary the ratio of the time the motor is connected to and disconnected from the supply means thereby to vary the mean power supplied to the motor, and differential means operatively connected to said ratio varying means to supply a variable input signal to at least one of said switching circuits for varying the said ratio for the circuit, thereby rendering different the mean power supplied to each motor.
 11. A drive system as claimed in claim 10, wherein one at least of said switching means comprises a relaxation oscillator including a capacitor and a transistor connected in parallel with the main thyristor, the degree of conduction of the transistor governing the rate of oscillation of the oscillator, said differential means being connected to the transistor to vary the degree of conduction of the transistor in dependence upon the variable input signal supplied by the differential means thereby to vary the rate of oscillation of the oscillator. 